Factor 3x^2-12x+12

Problem

3*x2−12*x+12

Solution

1. Factor out the greatest common factor which is 3 from all terms in the expression.

3*(x2−4*x+4)

2. Identify the quadratic pattern inside the parentheses, which is a perfect square trinomial of the form a2−2*a*b+b2

x2−4*x+4=(x)2−2*(x)*(2)+(2)2

3. Apply the perfect square formula (a−b)2=a2−2*a*b+b2 where a=x and b=2

(x−2)2

4. Combine the factors to write the final factored form of the original expression.

3*(x−2)2

Final Answer

3*x2−12*x+12=3*(x−2)2

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